= Integrating sphere
An \b[integrating sphere] is an optical cavity with diffusely reflecting interior walls and ports for illumination, samples or detectors. Repeated wall reflections mix the incident <radiant flux>, reducing sensitivity to where it first strikes. Baffles prevent a receiver from directly viewing an unwanted source or illuminated patch; port size and wall reflectance remain part of the response model.<Integrating Sphere Theory and Applications by Labsphere>[§§1.0–1.3, sphere theory and spatial integration; §2.3, baffles]{ref}
An original encounter model illustrates the effect of openings. Suppose a well-mixed reflection retains fraction $\rho$ and fraction $f$ of the reflected light escapes through ports before the next wall encounter. The <integrating-sphere port-loss factor> $1-f$ combines with wall reflectance to give a survival fraction $q=\rho(1-f)$. If the first wall encounter carries energy $U$, successive encounters carry $U,qU,q^2U,\ldots$, so their summed incident energy is $U/(1-q)$.
With stipulated $\rho=0.98$ and $f=0.02$, this sum is $25.25U$. Enlarging the openings to $f=0.05$ reduces it to $14.49U$. These are repeated encounters with the same initially supplied energy, not optical gain: absorption and escape together still account for that original energy. The example counts incident wall encounters from the first one and does not assert a calibrated detector multiplier.
An actual sphere measurement compares its detector signal with a calibrated input or reference. Coating wavelength dependence, ports, sample substitution and temporal response can affect the conversion. The primary guide discusses reflectance/transmittance arrangements and their measurement geometry.<Integrating Sphere Theory and Applications by Labsphere>[§§1.4 and3.2–3.2.2]{ref} An integrating sphere is therefore useful apparatus, rather than a guarantee that every outgoing component has been measured without correction.
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